Question

what number should added to each of the following number 3, 5, 13 and 19, so that the resulting number may be in proportion

Answer 1

let x be added to each number then all the 4 numbers will be in proportion

therefore , 3+x , 5+x , 13+x , 19+x are now in proportion

using proportionality ,

3+x / 5+x = 13+x / 19+x

(3+x) × (19+x) = (13+x) × (5+x)

57 +3x+19x+x^2 = 65+13x+5x+x^2

22x+57 = 18x + 65

22x - 18x = 65 - 57

4x = 8

x =2

therefore 2 should be added